Parity-Violating Effects in Few-Nucleon Systems

Transcription

1 Parity-Violating Effects in Few-Nucleon Systems Joe Carlson (LANL) Rocco Schiavilla (JLAB/ODU) Alejandro Kievsky (INFN-Pisa) Laura Marcucci (U-Pisa) Michele Viviani (INFN-Pisa) Mark Paris (JLAB) Ben Gibson (LANL) Virginia Brown (MIT-UMD) 1

2 Outline A realistic model of strong and electromagnetic interactions in nuclei: an update From PV observables to PV interactions in few-nucleon (mostly N N) systems: model dependence Effects of hadronic weak interactions in d( e, e )np at quasielastic kinematics Summary(I) Isospin mixing in the nucleon and 4 He and the PV asymmetry in 4 He( e, e ) 4 He Summary (II) 2

3 Nuclear Interactions NN interactions alone fail to predict: 1. spectra of light nuclei 2. Nd scattering 3. nuclear matter E 0 (ρ) 2π-N N N interactions: 2π A pw + Α 2π sw very weak EFT w/o explicit s overestimates strength of V 2π pw Pandharipande et al., PRC71, (2005) V 2π alone does not fix problems above 3

4 Proton-Deuteron Elastic Scattering Ermisch et al. (KVI collaboration), PRC71, (2005); Kalantar-Nayestanaki, private communication d /d [mb/sr] NN+TM 0.0 NN+UIX NN+Delta A y (d the -d exp )/d exp [% ] Ener gy [MeV ] KVI 2001 Syst. err A y the -Ay exp 4

5 Beyond 2π-exchange (IL2 model) V 2π + A 3π + + A R cyc T 2 (r ij ) T 2 (r jk ) parameters ( 3) fixed by a best fit to the energies of low-lying states of nuclei with A 8 AV18/IL2 Hamiltonian reproduces well spectra of A=9 12 nuclei but needs to be tested in three- and four-nucleon scattering (work by the Pisa group is in progress) A y puzzle in 4-body scattering: strong isospin dependence, discrepancy in 3 H-p or 3 He-n much reduced relative to 3 He-p (Deltuva and Fonseca, PRL98, (2007) and nucl-th/ ) 5

6 Nuclear Electromagnetic Currents j Marcucci et al., PRC72, (2005) = (1) j + j (2) (v) + + π π ρ,ω + j (3) (V 2π ) transverse Gauge invariant: q [ ] j (1) + j (2) (v) + j (3) (V 2π ) = [ ] T + v + V 2π, ρ ρ is the nuclear charge operator 6

7 Terms from static part v 0 of v: j ij (v 0 ; leading) = i (τ i τ j ) z [v P S (k j )σ i (σ j k j ) + k i k j k 2 i k2 j v P S (k i ) (σ i k i ) (σ j k j ) ] + i j with v P S = v στ 2 v tτ j (2) (v 0 ) satisfies: j (2) π π (v 0 ) + + π π long range 7

8 1 H(n,γ) 2 H capture Deuteron threshold photodisintegration AV18 σ γ (mb) x v(m/nsec) x AV18 BONN AV18 (M 1 only) EFT(M 1 to N 2 LO, E 1 to N 4 LO) σ γ (ω)(fm 2 ) BONN Data E n (kev) ω(mev) 8

9 2 H(p, γ) 3 He Radiative Capture at E 50 kev Marcucci et al., PRC72, (2005) Suppressed process, S- and P -wave capture both important 0.5 S(E) (ev b) LUNA Griffiths et al. Schmid et al E CM (kev) S(E = 0) (ev b) Theory LUNA 0.216±0.010 however, 2 H(n, γ) 3 H experimental cross section at thermal energies is overestimated by theory by 9 % 9

10 Constraining PV interactions A z in pp scattering A γ in np capture and P γ in d( γ, n)p Neutron spin rotation in np (and nα) scattering Experiment Hadronic Theory 10

11 Longitudinal Asymmetry in pp Scattering Liu et al., PRC73, (2006); Carlson et al., PRC65, (2002); Driscoll and Miller, PRC39, 1951 (1989) A z = [σ(+) σ( )]/[σ(+) + σ( )] M =scattering amplitude = Im [M(S = 0 or 1 S = 1 or 0)] PC potentials forbid S S = 1 transitions A z is the nuclear asymmetry, Coulomb effects need to be included 11

12 DDH model for PV potential: v PV = g [ ] ρ h pp { } ρ (σ 1 σ 2 ) p, Y ρ (r) + (1 + κ ρ )Y m ρ(r)σ 1 σ 2 ˆr g ω h pp ω m [ ρ ω ] with Y α (r) = 1 4π r [ e m αr e Λ αr [ ( ) ]] 1 m2 α Λ Λ 2 α r α v PV acts only in even J channels: at low and moderate T lab the 1 S 0-3 P 0 and 1 D 2-3 P 2 are the relevant PV mixings EFT version of v PV has same structure, but with Y (r) replaced by δ-function [Zhu et al., NPA748, 435 (2005)] 12

13 A z in pp Elastic Scattering BONN2000+DDH TRIUMF, A (10 7 ) Bonn, 79 AV18+DDH AV18+DDH best guess A (10-7 ) A (J=0) A (J=0) +A (J=2) PSI, T lab (MeV) T lab (MeV) A (J=0) h pp ρ g ρ (2+κ ρ )+h pp ω g ω (2+κ ω ) A (J=2) h pp ρ g ρ κ ρ +h pp ω g ω κ ω Strong correlation between h pp ρ and h pp ω 13

14 Sensitivity to modeling of short-range v PV (Λ ρ,λ ω )=(1.31,1.50) GeV/c (Λ ρ,λ ω )=(1.10,1.25) GeV/c point-like A (10-7 ) 0.0 A (10-7 ) (Λ ρ,λ ω )=(1.31,1.50) GeV/c (Λ ρ,λ ω )=(1.10,1.25) GeV/c point-like T lab (MeV) T lab (MeV) 14

15 Photon Asymmetry in 1 H( n, γ) 2 H Radiative Capture Measure correlation a γ cosθ between n spin and γ momentum: 2 Re (M a γ = 1 E 1 ) M 1 2 with M 1 : 1 S 0 ; PC d; PC well known transition E 1 : 3 S 1 ; PC d; PV 3 P 1 ; PV d; PC 3 P 1 PV wave functions in d and continuum dominated by v PV π : vπ PV (T = 0 T = 1) = i g π h π Y π(r) (σ 1 + σ 2 ) ˆr 2 m + vector meson terms 15

16 PC and PV Deuteron Wave Functions 0.6 PC 3 S PC 3 D 1 PV 1 P 1 (x10 7 ) PV 3 P 1 (x10 7 ) u LST (r)(fm -3/2 ) PV 3 P 1 (x10 7 ) no π in DDH r(fm) PC 3 S 1 PC 3 D PV 1 P 1 (x10 7 ) PV 3 P 1 (x10 7 ) 0.2 fm 1/2 0.2 fm 1/2 0.0 AV18 BONN AV r(fm) BONN r(fm) 16

17 Contributions to a γ (schematically): d c PV d c PV d c PV Impulse PC mec PV mec E 1 i dx ˆɛ j(x) Large cancellations between asymmetries induced by PV interactions and those due to the associated PV MEC Potentially large model dependence is minimized via Siegert evaluation of E 1 : E 1 ω γ dx ˆɛ x ρ(x) 17

18 σ γ (mb) a γ 10 8 Interaction Impulse Current Full Current DDHπ DDH AV BONN EXP 332.6±0.7??? In units of h π, a γ 0.11 h π in agreement with a number of recent calculations [Desplanques, PLB512, 305 (2001); Hyun et al., PLB516, 321 (2001)] 18

19 Helicity-Dependent Asymmetry in 2 H( γ, n)p Photodisintegration In the threshold region ( 1 kev above breakup): P γ = 2 Re ( M 1 E 1 ) M 1 2 E 1 : d( 1 P 1 ); PV 1 S 0 ; PC d; PC 3 P 0 ; PV v PV π does not contribute P γ exhibits large sensitivity to modeling of short range strong and weak N N interactions P γ in units of 10 8 AV18+DDH BONN+DDH AV18+DDHπ Impulse Full

20 At higher energies, remarks in previous slide remain valid: 2 0 P γ (ω)x AV18+DDH AV18+DDHπ(x10) BONN+DDH ω(mev) 20

21 Neutron Spin Rotation Transmission of a low energy neutron through matter: e ipz σ> e ip(z d) e ipdn σ σ> PV observable: d n σ = 1 + 2π ρ p 2 M σ(θ = 0) z z x y dφ dd = 2π ρ p Re [M +(θ = 0) M (θ = 0)] x φ y 21

22 dφ/dd in units of 10 9 rad/cm DDH DDHπ AV BONN Plane waves Earlier study [Avishai and Grange, JPG10, L263 (1984)] finds, incorrectly, the same sign w/ and w/o strong interaction leading term 3 S 1 v PV π 3 P 1 j(pr) j(pr) 0 1 u(3s1)u(3p1) v PV π v PV π 22

23 Neutron Spin Rotation in 4 He Pion PV Matrix Element GFMC <1/2 V π 1/2+ > τ (MeV 1 ) 23

24 d( e, e )np at quasielastic kinematics: SAMPLE Ito et al., PRL92, (2004) Physics Asymmetry (ppm) Q (GeV/c) 2 A th (Q 2 = 0.038GeV/c) = G s M G (e) A,T =1 A th (Q 2 = 0.091GeV/c) = G s M G (e) A,T =1 24

25 f,pc> * f,pc> γ Z γ + PV A = d,pc> d,pc> 2 + c.c. γ = A γγ + Α γz A γz well known, A γγ [ ] i,f Im j fi (γ) j fi (γ) A γγ (related to P γ at the photon point) originates from: z δ(ω + E i E f ) 1. Small PV components induced by v PV into PC states 2. j PV 2 associated with v PV 3. anapole contributions: a(q 2 )u (qq σ q 2 γ σ )γ 5 u/m 2 a(q 2 ) = g πh π 8 2π 2 (α S + α V τ z ) with estimates for α S and α V from either pion loops (Musolf et al.), or the quark model (Riska), or EFT (Maekawa and van Kolck) 25

26 Sample-III Kinematics 4 2 A γγ x body (1+2) body 4 2 induced by PV γ couplings A(E ) 0 2 A γz x10 6 A γγ (E )x induced by the DDH interaction E (MeV) E (MeV) A γγ two orders of magnitude smaller than A γz 26

27 Summary(I) A z ( pp) is weakly dependent on input v PC, but sensitive to short-range modeling of v PV A γ ( np) and, to a less extent, the neutron spin rotation provide the cleanest determination of h π P γ (d γ) is strongly affected by short-range modeling of both v PC and v PV PV electrodisintegration of the deuteron at quasielastic kinematics probes, almost exclusively, γz interference on individual nucleons Outlook: 1. GFMC studies of n- and p-α scattering 2. Possibly, HH studies of n 2 H and n 3 He radiative captures 27

28 4 He( e, e ) 4 He Scattering where A PV = G µq 2 4πα 2 4 He j µ=0 NC 4 He 4 He j µ=0 EM 4 He G µq2 4πα 2 4 s2 W j µ=0 EM = j(0) + j (1) j µ=0 NC = 4 s2 W j (0) + (2 4 s 2 W )j (1) j (s) A PV sensitive to G s E (Q2 ), provided negligible: 1. relativistic corrections (RC) and MEC contributions 2. isospin symmetry breaking (ISB) in the nucleon and 4 He At low Q 2, RC+MEC contributions calculated to be tiny a a Musolf, Schiavilla, and Donnelly, PRC50, 2173 (1994) 28

29 Parameterizing ISB in the nucleon Dmitrasinović and Pollock, PRC52, 1061 (1995); Kubis and Lewis, PRC74, (2006) In terms of the measured G p/n E = p/n jµ=0 EM p/n : (G p E + Gn E)/2 = G 0 E + G / 1 E (G p E Gn E)/2 = G 1 E + G / 0 E from which G p,z E = (1 4s2 W )G p E Gn E + 2(G / 1 E G/ 0 E ) Gs E G n,z E = (1 4s2 W )G n E G p E + 2(G/ 1 E + G/ 0 E ) Gs E where ISB in G s E are ignored: p j(s) p = n j (s) n G s E (Q2 ) 29

30 Nuclear EM and NC (Vector) Charge Operators ρ (EM) (q) = G p E Z e iq r k + G n E A e iq r k ρ (0) (q) + ρ (1) (q) k=1 k=z+1 ρ (0) (q) = Gp E + Gn E 2 ρ (1) (q) = Gp E Gn E 2 A k=1 e iq r k ( Z e iq r k k=1 A k=z+1 e iq r k ) With G p/n E Gp/n,Z E, ρ (NC) (q) can be written as ρ (NC) (q) = 4s 2 W ρ (EM) (q) + 2 G/ 1 E Gs E (G p E + Gn E )/2ρ(0) (q) +2ρ (1) (q) 2 G / 0 E (G p E Gn E )/2ρ(1) (q) 30

31 Up to linear terms in ISB corrections: [ ] A PV = G µq 2 4πα 4 s 2 W 2 F (1) (q) 2 F (0) (q) 2 G/1 E Gs E (G p E + + RC/MEC Gn E )/2 where 4 He ρ (a) (q) 4 He /Z F (a) (q), a = EM, 0, 1 The HAPPEX collaboration [PRL98, (2007)] reports: A PV [Q 2 = (GeV/c) 2 ] = [+6.40 ± 0.23 (stat) ± 0.12 (syst)]ppm from which, using G µ = GeV 2, α=1/ , and = (with radiative corrections), s 2 W Γ 2 F (1) (q) F (0) (q) 2 G/1 E Gs E (G p E + = ± Gn E )/2 31

32 ISB Corrections (I): Nucleon Kubis and Lewis, PRC74, (2006) Up to NLO in ChPT: 1. Loop effects due m = m n m p 2. A single counterterm, fixed by resonance saturation ρ ω 0 ω ρ 0 32

33 Kubis and Lewis, PRC74, (2006) G / 1 E (Q2 ) = g2 A m N m + Q2 2m 2 N F 2 π [ 1 16π 2 { M [ ] π γ m 0 ( Q 2 ) 4γ 3 ( Q 2 ) N ξ( Q 2 ) M [ ] π γ m 0 ( Q 2 ) 5γ 3 ( Q 2 ) N ( log M π g ω F ρ Θ ρω Q 2 2M V (M 2 V + Q2 ) 2 M V ) ]} π(κv + 6)M π 2m N ) ( 1 + κ ωm 2 V 4m 2 N γ 0, γ 3, and ξ are loop functions: Q 2 as Q 2 0 Largest uncertainty in ω tensor coupling κ ω 33

34 G E 1/ (Q 2 ) Q 2 [(GeV/c) 2 ] G M u,d (Q 2 ) ISB contributions to proton f.f. G E u,d (Q 2 ) Q 2 [(GeV/c) 2 ] Band provides an estimate of higher order ChPT corrections as well as of uncertainties in vector-meson couplings At Q 2 = (GeV/c) 2 : 2 G / 1 E (G p E + = ± Gn E )/2 34

35 ISB Corrections (II): 4 He Nucleus Nuclear ISB Hamiltonian: H ISB = H C + H CD/CA + H EM + K H C from (point) Coulomb interaction H CD/CA from CD and CA strong-interactions H EM from remaining EM interactions (magnetic moments,... ) K from n-p mass difference in kinetic energy Viviani, Kievsky, and Rosati, PRC71, (2005) ISB term (AV18) P (1) % P (2) % H C H C + H CD/CA H C + H CD/CA + H EM

36 Contributions of ISB terms to isomultiplet energies (kev) Pieper, Pandharipande, Wiringa, and Carlson, PRC64, (2001) A T n K H C H EM H CD/CA TOT EXP 3 1/2 1 14(0) 649(1) 29(0) 64(0) 757(1) (0) 1091(5) 18(0) 47(1) 1172(6) (0) 1686(5) 24(0) 76(1) 1810(6) (1) 19(0) 107(13) 293(13) (1) 4(0) 3(8) 143(8) 145 Good overall agreement between theory and experiment 36

37 F (1) (q)/f (0) (q) AV18/UIX (one-body) AV18/UIX (one-body+mec) F(q) AV18/UIX AV18 CDB-UIXb N3LO q(fm -1 ) F (0) (q) 10-4 F (1) (q) q(fm -1 ) Weak model dependence q F (1) scales as P (1) ; RC/MEC small at low q ( 1.5 fm 1 ) F (1) /F (0) from AV18/UIX and CDB/UIXb 37

38 Summary(II) Using: i) 2 G / 1 E /[(Gp E + Gn E )/2] for hadronic ISB in ii) 2 F (1) (q)/f (0) (q) for nuclear ISB Γ 2 F (1) (q) F (0) (q) 2 G/1 E Gs E (G p E + = ± Gn E )/2 gives G s E[ Q 2 = (GeV/c) 2] = ± Measuring ISB admixtures? (arguably... error on Γ too large!) G s E[ Q 2 = 0.1 (GeV/c) 2] = ± ± estimated by using LQCD input [Leinweber et al., PRL97, (2006)] At this level, contributions to A PV induced by PV components in the nuclear potentials need to be studied (competitive with ISB?) 38